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Math lesson plan · 8th grade (Year 9 in England) · 60 minutes

Interpret rate of change and initial value in context

Algebra

CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Interpret rate of change and initial value in context.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Write y = mx + b from a slope and intercept, or from a graph

Leads to: Compare two functions given in different ways; Interpret the slope and intercept of a line of best fit

Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Write y = mx + b from a slope and intercept, or from a graph). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Write the equation of the line with slope 7 and y-intercept 9. Type the right-hand side (y = …). → 7x+9Prompt: Use y = mx + b.
  2. Arjun says the line through (0, 5) with slope 5 is y = 5x + 5. Write the correct equation. Type the right-hand side. → 5x+5Prompt: Arjun swapped the slope and the intercept.
  3. Write the equation of the line with slope −5 and y-intercept 9. Type the right-hand side (y = …). → -5x+9Prompt: Use y = mx + b.

Hook · 6 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Interpret rate of change and initial value in context. Read the success criteria together.

I do: model it · 12 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A bamboo shoot is 10 cm tall and grows 10 cm per day. In y = mx + b, what is b?
  • Step 1: b = 10
  • Step 2: y = 10x + 10
  • Answer: 10
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 12 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. A bamboo shoot is 27 cm tall and grows 5 cm per day. In y = mx + b, what is b? → 27Prompt: m is the rate of change: how much per unit of time.
  2. A water tank holds 62 litres and drains at 8 litres per minute. Write the amount left after t minutes and find how much is left after 5 minutes. → 22Prompt: The rate of change is −8 (it goes down).

You do: independent practice · 17 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. The cost of a pottery class is C = 3h + 29, where h is hours. What does 29 represent? (The number of hours / The total cost for 29 hours / The cost per hour / A fixed fee paid even for 0 hours) → A fixed fee paid even for 0 hoursPrompt: Which number is multiplied by h?
  2. A bamboo shoot is 14 cm tall and grows 3 cm per day. In y = mx + b, what is b? → 14Prompt: m is the rate of change: how much per unit of time.

Watch out for

  • Doing an operation to one side of an equation but not the other.
  • Reading 3x as 3 + x, or thinking x always stands for one particular number.

Support and stretch

Support

  • Review first: Write y = mx + b from a slope and intercept, or from a graph.
  • Use concrete materials: balance scales or a balance drawing.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Compare two functions given in different ways; Interpret the slope and intercept of a line of best fit.
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.

Free lesson plan from eurekami.com/lesson-plan-builder

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Interpret rate of change and initial value in context

Name

Date

Score/ 8

  1. Question 1

    The cost of a pottery class is C = 9h + 6, where h is hours. What does 6 represent?

    • A. The cost per hour
    • B. The total cost for 6 hours
    • C. The number of hours
    • D. A fixed fee paid even for 0 hours

  2. Question 2

    A water tank holds 86 litres and drains at 3 litres per minute. Write the amount left after t minutes and find how much is left after 24 minutes.

    Answer

  3. Question 3

    A savings jar has 16 coins and 15 coins are added each week. In y = mx + b, what is b?

    Answer

  4. Question 4

    The cost of a pottery class is C = 8h + 19, where h is hours. What does 19 represent?

    • A. The cost per hour
    • B. The number of hours
    • C. A fixed fee paid even for 0 hours
    • D. The total cost for 19 hours

  5. Question 5

    A water tank holds 45 litres and drains at 2 litres per minute. Write the amount left after t minutes and find how much is left after 9 minutes.

    Answer

  6. Question 6

    A savings jar has 26 coins and 11 coins are added each week. In y = mx + b, what is m?

    Answer

  7. Question 7

    The cost of a pottery class is C = 7h + 28, where h is hours. What does 28 represent?

    • A. The cost per hour
    • B. The total cost for 28 hours
    • C. A fixed fee paid even for 0 hours
    • D. The number of hours

  8. Question 8

    A water tank holds 80 litres and drains at 8 litres per minute. Write the amount left after t minutes and find how much is left after 5 minutes.

    Answer

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Answer key: Interpret rate of change and initial value in context

  1. 1. D. A fixed fee paid even for 0 hours

  2. 2. 14

  3. 3. 16

  4. 4. C. A fixed fee paid even for 0 hours

  5. 5. 27

  6. 6. 11

  7. 7. C. A fixed fee paid even for 0 hours

  8. 8. 40